As seen above, the superfluid density takes a reduced value as if
only the doped carriers condense into the superconducting state.
Such behavior is reminiscent of underdoped cuprates,
in which the normal-state carrier density [1]},
the Drude weight [2]} and the superfluid density [3]}, [4]}
are discussed to be governed by the doped carriers.
Theoretically, such a significant reduction in the superfluid density is suggested to occur
when double occupancies of particles are strongly prohibited [5]}, [6]}, [7]}.
Previous transport studies on \(\kappa \) -HgBr at low pressures revealed that
the mobile carriers are in a quantum critical state with a spin-liquid background
[8]}, [9]}, [10]}, [11]},
which may bring about an incoherent part, preventing the entire spectral weight from
contributing to the conduction and/or superconducting condensate.
It is argued for underdoped cuprates that some competing or hidden orders are responsible for
the reduction in the superfluid density [12]} because various orders or
anomalies appear in the spin and charge degrees of freedom competing with
superconductivity [13]}, [14]}.
In this respect, \(\kappa \) -HgBr is distinct from cuprates in that
no such competing orders have ever been observed,
probably because a QSL free form order is the mother phase of the superconductivity.
Although in recent years the possibility of competing orders in doped triangular lattices
has theoretically suggested in certain parameter spaces [15]}, [16]},
the observation of a considerable reduction in the superfluid density without
apparent competing orders in the present system would offer a focused target to
diverse theoretical challenges with regard to the issue of missing superfluid spectral weight.
